Feed efficiency during lactation involves a set of phenotypic traits that form a complex system, with some traits exerting causal effects on the others. Information regarding such interrelationships can be used to predict the effect of external interventions on the system, and ultimately to optimize management practices and multi-trait selection strategies. Structural equation models can be used to infer the magnitude of the different causes of such interrelationships. The causal network necessary to fit structural equation models can be inferred using the inductive causation (IC) algorithm. By implementing these statistical tools, we inferred the causal association between the main energy sources and sinks involved in sow lactation feed efficiency for the first time, i.e., daily lactation feed intake (dLFI) in kg/day, daily sow weight balance (dSWB) in kg/day, daily litter weight gain (dLWG) in kg/day, daily back fat thickness balance (dBFTB) in mm/day, and sow metabolic body weight (SMBW) in kg 0.75 . Then, we tested several selection strategies based on selection indices, with or without dLFI records, to improve sow efficiency during lactation. The IC algorithm using 95% highest posterior density (HPD 95% ) intervals resulted in a fully directed acyclic graph, in which dLFI and dLWG affected dSWB, the posterior mean of the corresponding structural coefficients (PM λ ) being 0.12 and − 0.03, respectively. In turn, dSWB influenced dBFTB and SMBW, with PM λ equal to 0.70 and − 1.22, respectively. Multiple indirect effects contributed to the variances and covariances among the analyzed traits, with the most relevant indirect effects being those involved in the association between dSWB and dBFTB and between dSWB and SMBW. Selection strategies with or without phenotypic information on dLFI, or that hold this trait constant, led to the same pattern and similar responses in dLFI, dSWB, and dLWG. Selection based on an index including only dBFTB and dLWG records can reduce dLFI, keep dSWB constant or increase it, and increase dLWG. However, a favorable response for all three traits is probably not achievable. Holding the amount of feed provided to the sows constant did not offer an advantage in terms of response over the other strategies.